To analyze the thermodynamic properties of the reaction \( \text{CO} + 2\text{H}_2 \rightleftharpoons \text{CH}_3\text{OH} \), we consider several key thermodynamic quantities, such as the standard Gibbs free energy change (\( \Delta G^\circ \)), standard enthalpy change (\( \Delta H^\circ \)), and standard entropy change (\( \Delta S^\circ \)). Here's an overview of how these properties relate to the reaction at standard conditions (25 °C, 1 atm).
1. Standard Gibbs Free Energy Change (\( \Delta G^\circ \))
The Gibbs free energy change indicates the spontaneity of a reaction under standard conditions. If \( \Delta G^\circ < 0 \), the reaction is spontaneous in the forward direction, while if \( \Delta G^\circ > 0 \), it is non-spontaneous.
2. Standard Enthalpy Change (\( \Delta H^\circ \))
The standard enthalpy change for a reaction reflects the total heat content change when the reactants form products at standard conditions. For the reaction of CO with hydrogen to form methanol, this typically can be calculated or looked up in thermodynamic tables.
3. Standard Entropy Change (\( \Delta S^\circ \))
The standard entropy change indicates how the disorder of the system changes as reactants are converted to products. A positive \( \Delta S^\circ \) value suggests increased disorder, while a negative value indicates decreased disorder.
Reaction Data
The approximate standard values for the compounds involved typically, again, can be referenced from thermochemical data tables:
- \( \Delta H_f^\circ \) (Standard enthalpy of formation) for methanol (\( \text{CH}_3\text{OH} \)): about \(-238.7 , \text{kJ/mol}\)
- \( \Delta H_f^\circ \) for CO: \( -110.5 , \text{kJ/mol} \)
- \( \Delta H_f^\circ \) for \( \text{H}_2 \): \( 0 , \text{kJ/mol} \) (as it is in its elemental form)
Using Hess's Law, you can calculate \( \Delta H^\circ \): \[ \Delta H^\circ = \Delta H_f^\circ (\text{CH}_3\text{OH}) - [\Delta H_f^\circ (\text{CO}) + 2 \times \Delta H_f^\circ (\text{H}_2)] \] \[ \Delta H^\circ = -238.7 - [-110.5 + 2 \times 0] \approx -128.2 , \text{kJ/mol} \]
For entropy:
- You would look up the standard entropy values (\( S^\circ \)) for CO, \( H_2 \), and \( CH_3OH \).
The calculation is: \[ \Delta S^\circ = S^\circ (\text{products}) - S^\circ (\text{reactants}) \]
Summary of Key Points
- \( \Delta G^\circ \): Depends on \( \Delta H^\circ \) and \( \Delta S^\circ \), can be calculated using \( \Delta G^\circ = \Delta H^\circ - T \Delta S^\circ \) at a given temperature.
- \( \Delta H^\circ \) and \( \Delta S^\circ \) values provide insights into heat flow and disorder.
Note
To get exact values of \( \Delta G^\circ \), \( \Delta H^\circ \), and \( \Delta S^\circ \) for your specific temperature or pressure, you might need to consult detailed chemical thermodynamic tables or databases, as they can vary with conditions.
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